Problem

Energy cost for a Car The cost of the electricity…

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Problem 20 Medium Difficulty

$\begin{array}{l}{\text { Renting a Car At a certain car rental agency a compact car }} \\ {\text { rents for } \$ 30 \text { a day and } 10 \phi \text { a mile. }} \\ {\text { (a) How much does it cost to rent a car for 3 days if the car }} \\ {\text { is driven } 280 \text { mi? }} \\ {\text { (b) Find a formula that models the cost } C \text { of renting this car }} \\ {\text { for } n \text { days if it is driven } m \text { miles. }}\end{array}$
(c) If the cost for a 3 -day rental was $\$ 140,$ how many miles
was the car driven?

Answer

a) Since the rent of the car is $\$ 30$ per day, then in 3 days, the cost of the rent is $\$ 90 .$ With the additional rent of 10 cents per mile, then in 280 miles, the extra cost is $\$ 28 .$ Hence, the total cost is $\$ 118 .$
b) $C=30 n+0.10 m$
c) $\begin{aligned} 140 &=30(3)+0.10 m \\ 140 &=90+0.10 m \\ 0.10 m &=50 \\ m &=500 \text { miles. } \end{aligned}$

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Video Transcript

So this problem is set up by telling us that at a certain car rental agency, a compact car runs for $30 a day in 10 cents a mile. Part A asks us for what? The prices of renting a car for three days and driving it for a total of 280 miles. So first we're going to start with finding the cost of the days alone. So we know that it's give me $30 for each day. Time's a total of three days so we can do this because no $1 or one day is $30. So two days will be 30 times 23 days with 30 times three and so on. So the day rental is going to be a total of $90. Then we're going to calculate the price for the mileage that we're putting on the car. So we know that it's 10 cents a mile and we're going to convert this $2 so that everything is easier. So we're going to say $0.1. That's equivalent to 10 cents per mile. Times are 280 miles driven, and this is for the same reason as well, deploring the $30 per day times or three days. We're also multiplying our 10 cents from mild times 280 miles. Now it gives us a total of $28 for the mileage and then to calculate the total cost. We're just going to add thes to cost together, so it's going to be $90 plus $28. So our final cost is going to be $118. And then Part B asks us. Teo basically created model to represent this this function. So we're just going to use the steps that we didn't part, eh? Do you come up with our model? So we said that the total price which we will call see, is equal to the addition of the day's part, which is the 30 times three plus the miles part, which is the 30.1 times 280. So, like we said, the the day section is going to be $30 $30 times the number of days that we rent the car, which, according to the problem, is going to be represented by a variable end and then it's going to be a plus our second part over here, which is our 0.1. So our 10 cents or $0.1 times the number of miles that we drive the car, which is going to be represented by M according to this problem. So here are model is cost C equals 30 times and plus 300.1 times M. Then finally, part See is asking us that if the costs for a three day rental was $140 so we'll say three days, which means that and equals three and then the total price. So it's, I mean, see, according to our function that we found in part be over here, R C is given as $140. So for this far it we're just going Teo, plug these values into our function, our model that we found in part B and then we're going to solve for M because it's asking for the number of miles. Good question. The number of miles that we drove so plugging in C equals 140. Some 140 equals 30 times and which is three plus 0.1 m times the number of miles. So our first step, we're going to just simplify this term right here. So 140 equals 90 plus 0.1 em. And then we're going to subtract 90 from both sides of the equation. It's that way were moving towards isolating our M. So we're left with 50 equals 0.1 em. And then now, to fully isolate our M, we're going to divide both sides by 0.1 0.1 and we find that em number of miles equals 500 miles.

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